I used "Shift-Insert" earlier today with text copied from firefox and pasted into a terminal (vi) for a co-worker stuck with the same issue on 11.. Not sure what needs to be changed in gvim to sync up the clipboards.

@Hamish's answer is nice and works fine for VIM. Another way, perhaps more general, is to use xclip (apt-get install xclip).

Run this (or, more realistically, bind it to some key):

xclip -selection clipboard -o | xclip -selection primary -i

It will take your clipboard (where things end up after pressing ctrl-C, generally) and move it to your primary X selection (what you paste when you press the middle mouse button). So you can then press the middle mouse button to paste into VIM, GVIM or any other application.